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REPORTS > KEYWORD > EXPANDER GRAPH:
Reports tagged with Expander Graph:
TR04-094 | 10th November 2004
Omer Reingold

Undirected ST-Connectivity in Log-Space

We present a deterministic, log-space algorithm that solves
st-connectivity in undirected graphs. The previous bound on the
space complexity of undirected st-connectivity was
log^{4/3}() obtained by Armoni, Ta-Shma, Wigderson and
Zhou. As undirected st-connectivity is
complete for the class of problems solvable by symmetric,
non-deterministic, log-space computations (the class SL), ... more >>>


TR13-007 | 8th January 2013
Bruno Bauwens, Anton Makhlin, Nikolay Vereshchagin, Marius Zimand

Short lists with short programs in short time

Revisions: 1

Given a machine $U$, a $c$-short program for $x$ is a string $p$ such that $U(p)=x$ and the length of $p$ is bounded by $c$ + (the length of a shortest program for $x$). We show that for any universal machine, it is possible to compute in polynomial time on ... more >>>


TR15-078 | 4th May 2015
Mladen Mikša, Jakob Nordström

A Generalized Method for Proving Polynomial Calculus Degree Lower Bounds

We study the problem of obtaining lower bounds for polynomial calculus (PC) and polynomial calculus resolution (PCR) on proof degree, and hence by [Impagliazzo et al. '99] also on proof size. [Alekhnovich and Razborov '03] established that if the clause-variable incidence graph of a CNF formula F is a good ... more >>>


TR19-011 | 27th January 2019
Benny Applebaum, Eliran Kachlon

Sampling Graphs without Forbidden Subgraphs and Almost-Explicit Unbalanced Expanders

Revisions: 3

We initiate the study of the following hypergraph sampling problem: Sample a $d$-uniform hypergraph over $n$ vertices and $m$ hyperedges from some pseudorandom distribution $\mathcal{G}$ conditioned on not having some small predefined $t$-size hypergraph $H$ as a subgraph. The algorithm should run in $\mathrm{poly}(n)$-time even when the size of the ... more >>>


TR19-112 | 1st September 2019
Yotam Dikstein, Irit Dinur

Agreement testing theorems on layered set systems

We introduce a framework of layered subsets, and give a sufficient condition for when a set system supports an agreement test. Agreement testing is a certain type of property testing that generalizes PCP tests such as the plane vs. plane test.

Previous work has shown that high dimensional expansion ... more >>>


TR20-163 | 5th November 2020
Gil Cohen, Noam Peri, Amnon Ta-Shma

Expander Random Walks: A Fourier-Analytic Approach

In this work we ask the following basic question: assume the vertices of an expander graph are labelled by $0,1$. What "test" functions $f : \{ 0,1\}^t \to \{0,1\}$ cannot distinguish $t$ independent samples from those obtained by a random walk? The expander hitting property due to Ajtai, Komlos and ... more >>>


TR21-099 | 4th July 2021
Louis Golowich

Improved Product-Based High-Dimensional Expanders

High-dimensional expanders generalize the notion of expander graphs to higher-dimensional simplicial complexes. In contrast to expander graphs, only a handful of high-dimensional expander constructions have been proposed, and no elementary combinatorial construction with near-optimal expansion is known. In this paper, we introduce an improved combinatorial high-dimensional expander construction, by modifying ... more >>>


TR22-154 | 6th November 2022
Gil Cohen, Itay Cohen

Spectral Expanding Expanders

Dinitz, Schapira, and Valadarsky (Algorithmica 2017) introduced the intriguing notion of expanding expanders -- a family of expander graphs with the property that every two consecutive graphs in the family differ only on a small number of edges. Such a family allows one to add and remove vertices with only ... more >>>


TR23-089 | 15th June 2023
Louis Golowich

New Explicit Constant-Degree Lossless Expanders

Revisions: 1

We present a new explicit construction of onesided bipartite lossless expanders of constant degree, with arbitrary constant ratio between the sizes of the two vertex sets. Our construction is simpler to state and analyze than the prior construction of Capalbo, Reingold, Vadhan, and Wigderson (2002).

We construct our ... more >>>


TR23-209 | 23rd December 2023
Yotam Dikstein, Irit Dinur

Swap cosystolic expansion

Revisions: 1

We introduce and study swap cosystolic expansion, a new expansion property of simplicial complexes. We prove lower bounds for swap coboundary expansion of spherical buildings and use them to lower bound swap cosystolic expansion of the LSV Ramanujan complexes. Our motivation is the recent work (in a companion paper) showing ... more >>>


TR24-013 | 26th January 2024
Oded Goldreich

On locally-characterized expander graphs (a survey)

Revisions: 1

We consider the notion of a local-characterization of an infinite family of unlabeled bounded-degree graphs.
Such a local-characterization is defined in terms of a finite set of (marked) graphs yielding a generalized notion of subgraph-freeness, which extends the standard notions of induced and non-induced subgraph freeness.

We survey the work ... more >>>




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